I need to accurately measure a narrow band signal (of about 200Hz) centered in a part of spectrum that is many times its band (at about 20kHz). I have only a 12 bit ADC that is relatively fast (5 MSPS). Can I perform something like this:

1. Sample & hold the signal at more than 2*B as required by the Nyquist theorem but undersampling with respect to the center frequency
2. Add some gaussian noise (dithering)
3. Oversample the (alias) signal and filter it in the digital domain to increase the total ADC resolution

Does it make sense?

• Were you planning on preceding the ADC with a narrow bandpass filter? Noise will get aliased too. Commented Jan 2, 2016 at 1:09
• Yes, of course I have to take care of out-of-band noise in this way Commented Jan 2, 2016 at 1:11
• You cannot determine which alias zone an undersampled signal is from after sampling (unless you already know, of course). Normally, you want to reduce the bandwidth of the sampled signal so that the total bandwidth of the signal is less than f/2. Can you please edit the question to include a specific proposed sampling frequency, to make the question clearer? Commented Jan 2, 2016 at 1:12
• What property of the signal are you trying to measure? Frequency or amplitude or?? Commented Jan 2, 2016 at 1:13
• I need to measure the amplitude of the signal (and then use a fft to extrapolate spectral content, but this is not part of this question). I want to have an alias of my signal in the first Nyquist zone, I still haven't done the calculations as I still have to decide what is the band and the central frequency of the signal to be measured. Commented Jan 2, 2016 at 1:16

Since your ADC is already more than fast enough, it would be far better to do all of the filtering, decimating, averaging, etc. that you're talking about in the digital domain, rather than in the analog domain. Then all you need in the analog domain is a low-pass filter that meets the antialiasing requirements of the ADC's actual sample rate.

EDIT: OK, I finally have an idea of what you're trying to accomplish. This is why a diagram is so much better than words. Here's my interpretation of what you're saying:

simulate this circuit – Schematic created using CircuitLab

The idea is to use dithering and oversampling to increase the effective resolution on each of the analog S/H output samples.

But you can get the same effect in the digital domain this way:

simulate this circuit

This is much simpler, and doing the narrow bandpass filter in the digital domain gives you much better control over its characteristics.

That filter implicitly gives you increased output resolution relative to the raw ADC resolution, because each output sample of the filter is a function of many input samples. In fact, making the bandwidth narrower means that more input samples contribute to each output sample. As long as the input signals aren't synchronous with the ADC clock in some way, they will be "self-dithering" in the sense that the quantization errors (at the ADC sample rate) will be uniformly distributed.

This is the same idea that is used in delta-sigma converters, in which a 1-bit raw ADC resolution is turned into a 24-bit (or more) output resolution by means of digital filtering and decimating.

• Yes, it is very perplexing why the OP doesn't want to just sample the signal at well over 40 kHz in the first place. Commented Jan 2, 2016 at 1:46
• I want to do this in order to increase the resolution of the ADC. If I undersample the signal with the S&H I have more time to collect samples which means a greater number of samples useful to increase the ADC resolution. Commented Jan 2, 2016 at 1:51
• @KBowser, maybe others are following what you mean. I am not following. I am not a DSP person, so it is possible that you know what you are talking about and I don't. But "undersample with the sample and hold" sounds like techno-babble to me. Commented Jan 2, 2016 at 8:07
• @KBowser, to increase the resolution of an ADC, you do it by oversampling, not by undersampling. to the extent that your DSP or CPU can handle it, sample this son-of-a-bitch as fast as you possibly can. at 5 MHz, if the ADC allows that (and your CPU can handle a short biquad filtering routine at 5 MSPS). there might be enough analog noise in your front end that the input is already sufficiently dithered. so filter out the out-of-band noise, heterodyne the bandpass signal down to baseband, then decimate, reducing the sample rate. Commented Jan 2, 2016 at 18:40

My gut reaction is that if the overall signal mix extends to 20Khz, any under sampling trick you attempt to measure your embedded 200hz is not going to work. I think you're going to have to either properly sample at 2X or better (40Khz + ) and then apply fast Fourier transform techniques to extract and measure the 200hz, Or, since you're talking about a 100/1 frequency ratio, a simple 2 or 3 pole analog filter (simple meaning 12db/octave or 18db/octave is more than sufficient), might then allow you to sample far under the full 20khz bandwidth without complication, having effective screened all frequencies outside your area of interest.

• Yes I want to isolate the important part of the signal using a bandpass filter so that the alias image extracted by the undersampling is as free of noise as possible. Commented Jan 2, 2016 at 1:21
• If you are adding an analog bandpass filter, especially if it is reasonably narrow and centered on the one frequency of interest, then your signal is no longer "centered" within 20khz at all anymore, because you've eliminated it right? So then its really not under-sampling to ignore the bandwidth you've screened out. At least within 12 bits. Of course if you were using a 16 bit sampler, that bandpass filter might need to be followed by brickwall filter. Commented Jan 2, 2016 at 1:34
• Basically I want to be able to collect more samples of the signal coming out from the sample&hold circuit in order to use oversampling and filtering to increase the ADC resolution. The starting point is that signal with important frequencies only in that band. I have to filter out the unwanted frequencies out of that band, "freeze" the alias signal using sample and hold (following the undersampling theory) and then recover a high resolution digital representation of that alias image through oversampling and filtering. I hope this is clearer now. Commented Jan 2, 2016 at 1:43
• i wouldn't put a S/H circuit on the analog input at all. just oversample this, filter out the out-of-band noise, heterodyne bandpass signal down to baseband, then decimate (or "down sample"). Commented Jan 2, 2016 at 18:48

If you properly filter all of the out-of-band noise before the ADC, you can use an undersampling technique to retrieve the signal as if it were below the Nyquist frequency by taking advantage of the 'alias image' property. This Wikipedia article goes into the details better than I ever could.

I'm not sure what exactly you're asking, but it sounds too similar to this not to point it out.